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  2. Schwarzschild coordinates - Wikipedia

    en.wikipedia.org/wiki/Schwarzschild_coordinates

    The extension of the exterior region of the Schwarzschild vacuum solution inside the event horizon of a spherically symmetric black hole is not static inside the horizon, and the family of (spacelike) nested spheres cannot be extended inside the horizon, so the Schwarzschild chart for this solution necessarily breaks down at the horizon.

  3. Schwarzschild metric - Wikipedia

    en.wikipedia.org/wiki/Schwarzschild_metric

    The Schwarzschild solution, taken to be valid for all r > 0, is called a Schwarzschild black hole. It is a perfectly valid solution of the Einstein field equations, although (like other black holes) it has rather bizarre properties. For r < r s the Schwarzschild radial coordinate r becomes timelike and the time coordinate t becomes spacelike. [22]

  4. Kruskal–Szekeres coordinates - Wikipedia

    en.wikipedia.org/wiki/Kruskal–Szekeres_coordinates

    The black hole event horizon bordering exterior region I would coincide with a Schwarzschild t-coordinate of + while the white hole event horizon bordering this region would coincide with a Schwarzschild t-coordinate of , reflecting the fact that in Schwarzschild coordinates an infalling particle takes an infinite coordinate time to reach the ...

  5. Gullstrand–Painlevé coordinates - Wikipedia

    en.wikipedia.org/wiki/Gullstrand–Painlevé...

    Gullstrand–Painlevé coordinates are a particular set of coordinates for the Schwarzschild metric – a solution to the Einstein field equations which describes a black hole. The ingoing coordinates are such that the time coordinate follows the proper time of a free-falling observer who starts from far away at zero velocity, and the spatial ...

  6. Eddington–Finkelstein coordinates - Wikipedia

    en.wikipedia.org/wiki/Eddington–Finkelstein...

    In general relativity, Eddington–Finkelstein coordinates are a pair of coordinate systems for a Schwarzschild geometry (e.g. a spherically symmetric black hole) which are adapted to radial null geodesics. Null geodesics are the worldlines of photons; radial ones are those that are moving directly towards or away from the central mass.

  7. Gravitational singularity - Wikipedia

    en.wikipedia.org/wiki/Gravitational_singularity

    An example is the Schwarzschild solution that describes a non-rotating, uncharged black hole. In coordinate systems convenient for working in regions far away from the black hole, a part of the metric becomes infinite at the event horizon .

  8. De Sitter–Schwarzschild metric - Wikipedia

    en.wikipedia.org/wiki/De_Sitter–Schwarzschild...

    Unlike a flat-space black hole, there is a largest possible de Sitter black hole, which is the Nariai spacetime (named after Hidekazu Nariai ). The Nariai limit has no singularities , the cosmological and black hole horizons have the same area, and they can be mapped to each other by a discrete reflection symmetry in any causal patch.

  9. Schwarzschild radius - Wikipedia

    en.wikipedia.org/wiki/Schwarzschild_radius

    (Supermassive black holes up to 21 billion (2.1 × 10 10) M ☉ have been detected, such as NGC 4889.) [17] Unlike stellar mass black holes, supermassive black holes have comparatively low average densities. (Note that a (non-rotating) black hole is a spherical region in space that surrounds the singularity at its center; it is not the ...